A participant in a SIMPLE IRA wants to make a traditional IRA contribution, and take the deduction. Is this possible?

Is a SIMPLE IRA considered a qualified plan for this purpose?

The participant may make an IRA contribution, providing he/she has eligible compensation.
A SIMPLE IRA is treated as an employer for the purpose of determining deductibility. The participant will be considered “active” for the years the contribution is attributable to, for instance, if the employer makes a non-elective contribution for 2002 in 2003, the participant is “active for 2002

Check out the following article for more information
Traditional IRA Deductibility Limits